Faraday rotator

ABSTRACT

Disclosed is a Faraday rotator capable of reducing the temperature dependence on a Faraday rotation angle, thereby enhancing the temperature characteristic, particularly, in a service environment in which the magnetization direction is variable, and an optical device using the Faraday rotator. The Faraday rotator includes a Faraday element which rotates the polarization plane of polarized light rays passing through the Faraday element when an external magnetic field is applied to the Faraday element. In this Faraday rotator, assuming that an angle between a magnetization direction of the Faraday element and a light ray direction is taken as α, the amount of the temperature-dependent change in Faraday rotation angle is reduced by applying the external magnetic field in a direction in which a first amount of the change in Faraday rotation angle due to the temperature dependence on the angle α and a second amount of the change in Faraday rotation angle due to the temperature dependence on the Faraday effect satisfy a relationship in which the sign of the first amount is plus or minus, the sign of the second amount is minus or plus, and the absolute value of one of the first and second amounts is less than twice the absolute value of the other amount, more preferably, substantially equal to the absolute value of the other amount.

BACKGROUND OF THE INVENTION

1. Technical Field of the Invention

The present invention relates to a Faraday rotator in which a Faradayelement and an external magnetic rield applying means are arranged suchthat the magnetization direction of the Faraday element is tilted withrespect to a light ray direction, and particularly to a Faraday rotatorcapable of reducing the amount of the temperature-dependent change inFaraday rotation angle by making use of the temperature dependence on anangle α between the magnetization direction of the Faraday element andthe light ray direction. Such a Faraday rotator is useful for variousoptical devices utilizing the Faraday effect, such as an opticalattenuator, and an optical isolator.

2. Related Art

Optical communication systems require an optical isolator for allowinglight rays to pass therethrough only in one direction, an opticalattenuator for controlling the quantity of light rays passingtherethrough, etc., and a Faraday rotator for rotating the polarizationplane of light rays passing therethrough is incorporated in the opticalisolator, optical annenuator, etc. The Faraday rotator is also used forother optical devices such as an optical switch, optical circulator,optical filter, and optical equalizer.

An optical isolator has a configuration, for example, shown in FIGS. 21Aand 21B in which a 45° Faraday rotator 3 is inserted between a polarizer1 and an analyzer 2 which are arranged such that the polarization planesof light rays passing through the polarizer 1 and analyzer 2 intersectone another at 45°. The Faraday rotator 3 includes a Faraday elementcomposed of a magnetooptic crystal in combination with a permanentmagnet as an external magnetic field applying means. An externalmagnetic field is applied to the Faraday element by the permanent magnetin such a manner as to correspond to a light ray direction, to realize amagnetic saturation state of the magnetooptic crystal. The magnetoopticcrystal is designed to have a thickness allowing the polarization planeof light rays passing therethrough to be rotated 45° in the abovemagnetic saturation state. When light rays are allowed to pass throughthe optical isolator in the forward direction, the light rays havingpassed through the polarizer 1 pass through the analyzer 2 almost withno loss (see FIG. 21A). On the contrary, when light rays are allowed topass through the optical isolator in the reverse direction, the lightrays having passed through the analyzer 2 cannot pass through thepolarizer 1 because the polarization plane of the light rays havingpassed through the Faraday rotator 3 are rendered perpendicular to thepolarizer 1 (see FIG. 21B). This optical isolator is of apolarization-dependent type; however, there is also known apolarization-independent type (see Japanese Patent Application No. Sho56-148290).

One example of a prior art optical attenuator is shown in FIGS. 2A and2B. As shown in FIG. 2A, a polarizer 14 composed of a wedge-shapedbirefringent crystal (for example, rutile), a Faraday rotator 15, and ananalyzer 16 composed of a wedge-shaped birefringent crystal 16 arearranged on the optical axis in this order between an input fiber 12having a collimate lens 10 and an output fiber 13 having a collimatelens 11 (see Japanese Patent Application No. Hei 4-205044). The Faradayrotator 15 includes, as shown in FIG. 2B, a Faraday element(magnetooptic crystal) 17 in combination with a permanent magnet 18 andan electromagnet 19 for applying magnetic fields to the Faraday element17 in two directions which are 90° offset from each other. Themagnetization direction of the Faraday element 17 is matched with thedirection of a synthetic magnetic field of a specific magnetic fieldapplied by the permanent magnet 18 and a variable magnetic field appliedby the electromagnet 19. Therefore, the Faraday rotation angle isvariable.

For example, when the polarizer 14 and the analyzer 16 are arranged suchthat the optical axes of both the birefringent crystals thereof arerendered parallel to each other, the optical attenuator operates asfollows. Light rays having gone out of the input fiber 12 are convertedinto a collimated light beam through the first lens 10 and are separatedinto an ordinary light ray o and an extraordinary light ray e throughthe polarizer 14. The polarization direction of the ordinary light ray ois perpendicular to that of the extraordinary light ray e. When thelight rays o and e pass through the Faraday rotator 15, the polarizationdirection of each of the light rays o and e is rotated depending on themagnitude of a component of the magnetization of the Faraday element 17in the direction parallel to the optical axis. The light rays o and eare then separated, through the analyzer 16, into an ordinary light rayo₁ and an extraordinary light ray e₁, and an ordinary light ray o₂ andan extraordinary light ray e₂, respectively. As shown by solid lines inFIG. 2A, the ordinary light ray o₁ and extraordinary light ray e₂outgoing from the analyzer 16 are parallel to each other, and arecoupled to the output fiber 13 through the second lens 11. Meanwhile, asshown by broken lines in FIG. 2A, the extraordinary light ray e₁ andordinary light ray o₂ outgoing from the analyzer 16 are not parallel toeach other but spread outwardly, and are not coupled to the output fiber13 through the second lens 11.

When the magnetic field applied to the Faraday element 17 by theelectromagnet 19 comes into zero, that is, when the magnetizationdirection of the Faraday element 17 is rendered parallel to the opticalaxis, the Faraday rotation angle of the Faraday element 17 becomes 90°.At this time, the ordinary light ray o having gone out of the polarizer14 goes out of the analyzer 16 as the extraordinary light ray e₁. Theextraordinary light ray e having gone out of the polarizer 14 goes outof the analyzer 16 as the ordinary light ray o₂. The light rays e₁ ando₂ are spread outwardly, and are not coupled to the output fiber 13through the second lens 11. On the contrary, when the magnetic fieldapplied to the Faraday element 17 by the electromagnet 19 becomessufficiently large, the Faraday rotation angle of the Faraday element 17comes closer to 0°. At this time, almost all of the ordinary light ray ohaving gone out of the polarizer 14 goes out of the analyzer 16 as theordinary light ray o₁, and almost all of the extraordinary light ray ehaving gone out of the polarizer 14 goes out of the analyzer 16 as theextraordinary light ray e₂. The light rays o₁ and e₂ are parallel toeach other, and are all coupled to the output fiber 13 through thesecond lens 11. The magnetization of the Faraday element 17 is thusrotated depending on the strength of the magnetic field applied to theFaraday element 17 by the electromagnet 19, to change the Faradayrotation angle of the Faraday element 17 in a range of about 90 to about0°, thereby making variable the quantity of the light rays coupled tothe output fiber 13 in accordance with the amount of the change inFaraday rotation angle. In this way, the above configuration includingthe Faraday rotator 15 functions as an optical attenuator.

It should be noted that if the polarizer 14 and the analyzer 16 arearranged such that the optical axes of both the birefringent crystalsthereof are perpendicular to each other, the optical attenuator operatesin accordance with the manner reversed to that described above. That isto say, when the Faraday rotation angle of the Faraday element 17becomes 90°, the quantity of light rays passing through the opticalattenuator is maximized, while when the Faraday rotation angle of theFaraday element 17 becomes zero, the quantity of light rays passingthrough the optical attenuator is minimized.

As the Faraday element to be incorporated in the Faraday rotator, therehas been, in recent years, used a Bi (bismuth) substitution rare earthelement-iron garnet single crystal film (LPE film) which has been mainlymanufactured by the LPE (Liquid Phase Epitaxial) Method. The reason forthis is that the LPE film has a large advantage that the Faradayrotation coefficient is larger than that of a YIG (yttrium-iron garnet)single crystal by the effect of addition of Bi.

The Bi substitution rare earth element-iron garnet single crystal,however, has a disadvantage in that the temperature dependence on theFaraday rotation angle is large. This causes a problem in increasing thetemperature dependence on the Faraday rotator, thereby making large thetemperature characteristic of an optical device manufactured using theFaraday rotator, such as an optical isolator or optical attenuator.

To improve the above-described temperature characteristic of the Faradayrotator, there have been typically proposed the following three methods:

(1) to improve the physical properties of the conventional crystal byreplacing it with a crystal having a special composition (JapanesePatent Application No. Sho 60-243217);

(2) to improve the temperature dependence on the Faraday rotator byusing two garnet crystals as a magnetooptic element for canceling thetemperature dependence on the Faraday rotation angle of one garnetcrystal by that of the other garnet crystal (Japanese Patent ApplicationNos. Sho 60-134372 and Hei 2-180757); and

(3) to improve the temperature characteristic of an optical device usinga Faraday rotator, a polarizer and an analyzer by optimally arrangingthe polarizer and the analyzer (Japanese Patent Application No. Hei8-45231).

The above proposed methods, however, have the following problems:

In the method (1), the temperature dependence on the Faraday rotationangle is reduced by adding Tb to the Bi substitution rare earthelement-iron garnet crystal as the magnetooptic element. However, anoptical isolator described in the embodiment is configured such that thethickness of a magnetooptic element of the optical isolator at awavelength of 1.5 μm at which the temperature dependence is minimizedbecomes about 1,700 μm. This thickness is excessively large inconsideration of the fact that the critical film thickness of a crystalallowed to be grown by the LPE method with its quality highly kept isabout 500 μm.

In the method (2), since two different garnet crystals must bemanufactured, the manufacturing cost becomes high.

In the method (3), an optical attenuator is realized by making use ofthe fact that the maximum light attenuation point (amount) in a statethat the polarization plane of light rays is perpendicular to thepolarizer is sensitive to the angle of the polarization plane, that is,the Faraday rotation angle, while the maximum light transmission point(amount) in a state that the polarization plane of light rays isparallel to the analyzer is insensitive to the Faraday rotation angle.That is to say, in the optical attenuator, the temperature dependence oneach of the maximum amount of light attenuation and insertion loss(maximum amount of light transmission) is made smaller by making thepolarization plane of light rays parallel to the analyzer when theFaraday rotation angle is maximized (at this time, the absolute value ofthe amount of the change in Faraday rotation angle is maximized); andmaking the polarization plane of light rays perpendicular to theanalyzer when the Faraday rotation angle is minimized (at this time, theabsolute of the amount of the change in the Faraday rotation angle isminimized). However, since the maximum light attenuation point issensitive to the Faraday rotation angle, the temperature dependence onthe Faraday rotation angle must be made very small at the maximum lightattenuation point, but the reduction in temperature dependence has alimitation because the Faraday rotator essentially has the temperaturedependence.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a technique of reducingthe temperature dependence on a Faraday rotation angle on the basis of anew principle.

Another object of the present invention is to provide a Faraday rotatorcapable of reducing the temperature dependence on the Faraday rotationangle.

A further object of the present invention is to provide an opticaldevice such as an optical attenuator improved in temperaturecharacteristic by using the Faraday rotator.

To achieve the above objects, according to a first aspect of the presentinvention, there is provided a Faraday rotator including: a Faradayelement which rotates the polarization plane of polarized light rayspassing through the Faraday element when an external magnetic field isapplied to the Faraday element, wherein assuming that an angle between amagnetization direction of the Faraday element and a light ray directionis taken as α, the amount of the temperature-dependent change in Faradayrotation angle is reduced by applying an external magnetic field in adirection in which a first amount of the change in Faraday rotationangle due to the temperature dependence on the angle α and a secondamount of the change in Faraday rotation angle due to the temperaturedependence on the Faraday effect satisfy a relationship in which thesign of the first amount is plus or minus, the sign of the second amountis minus or plus, and the absolute value of one of the first and secondamounts is less than twice the absolute value of the other amount, morepreferably, substantially equal to the absolute value of the otheramount.

According to a second aspect of the present invention, there is provideda Faraday rotator including: a Faraday element composed of a single or aplurality of magnetooptic crystals, which rotates the polarization planeof polarized light rays passing through the Faraday element when anexternal magnetic field is applied to the Faraday element, whereinassuming that an angle between a magnetization direction of the singleor plurality of magnetooptic crystals and a light ray direction is takenas α, the amount of the temperature-dependent change in Faraday rotationangle is reduced by applying an external magnetic field in a singledirection in which a first amount of the change in Faraday rotationangle due to the temperature dependence on the angle α and a secondamount of the change in Faraday rotation angle due to the temperaturedependence on the Faraday effect satisfy a relationship in which thesign of the first amount is plus or minus, the sign of the second amountis minus or plus, and the absolute value of one of the first and secondamounts is less than twice the absolute value of the other amount.

According to a third aspect of the present invention, there is provideda Faraday rotator including: a Faraday element composed of a pluralityof magnetooptic crystals arranged with their crystal orientations madedifferent from each other, which rotates the polarization plane ofpolarized light rays passing through the Faraday element when anexternal magnetic field is applied to the Faraday element, whereinassuming that angles between magnetization directions of themagnetooptical crystals and a light ray transmission direction are takenas α₁, α₂, α₃, . . . , the amount of the temperature-dependent change inFaraday rotation angle is reduced by applying an external magnetic fieldin a direction in which the absolute value of the sum of amounts of thechanges in Faraday rotation angle due to the temperature dependencies onthe angles α₁, α₂, α₃, . . . , and an amount of the change in Faradayrotation angle due to the temperature dependence on the Faraday effectis equal to or less than the absolute value of the sum of amounts of thechanges in Faraday rotation angle due to the temperature dependencies onthe Faraday effect of the magnetooptic crystals.

As described above, according to the present invention, the use of thetemperature dependence on magnetocrystalline anisotropy of amagnetooptic crystal used for a Faraday element makes it possible tocancel the amount of the change in Faraday rotation angle due to thetemperature dependence on an angle between the magnetization directionof a magnetooptic crystal and a light ray direction by the amount of thechange in Faraday rotation angle due to the temperature dependence onthe Faraday effect, and hence to obtain an effect of reducing the amountof the change in Faraday rotation angle even in a service environment inwhich the magnetization direction of the Faraday element is changed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are illustrative diagrams showing a relationship betweena magnetization direction of a magnetic garnet single crystal of thepresent invention and a light ray direction;

FIGS. 2A and 2B are illustrative diagrams showing one example of a priorart optical attenuator;

FIG. 3 is an illustrative diagram showing a measurement system used inthe present invention;

FIG. 4 is an illustrative diagram showing one example of a Faradayrotator shown in FIG. 3;

FIGS. 5A to 5D are illustrative diagrams showing manufacturing steps,shape of a final product, and orientation of a magnetic garnet singlecrystal;

FIG. 6 is a stereographic projection chart centered at the (111) planeof a magnetic garnet single crystal;

FIG. 7 is a graph showing a relationship between a current value and aFaraday rotation angle in the case where a magnetic field is appliedalong a route “a”;

FIG. 8 is a graph showing a relationship between a current value and aFaraday rotation angle in the case where a magnetic field is appliedalong a route “b”;

FIG. 9 is a graph showing a relationship between a current value and aFaraday rotation angle in the case where a magnetic field is appliedalong a route “c”;

FIG. 10 is a graph showing a relationship between a current value and aFaraday rotation angle in the case where a magnetic field is appliedalong a route “d”;

FIG. 11 is a sectional view showing a relationship between a magneticfield, a magnetization direction and a crystal orientation in the casewhere a magnetic field is applied along a route “a”;

FIGS. 12A and 12B are illustrative diagrams showing an arrangementdirection of magnetic garnet single crystals used for a Faraday element;

FIG. 13 is a graph showing a relationship between a temperature and aFaraday rotation angle for each of a first embodiment and a comparativeexample A;

FIG. 14 is a graph showing a relationship between a temperature and anamount of light attenuation for each of the first embodiment and thecomparative example A;

FIG. 15 is a graph showing a relationship between a current value of anelectromagnet and a Faraday rotation angle in a second embodiment;

FIG. 16 is a graph showing a relationship between a current value of anelectromagnet and an amount of light attenuation in the secondembodiment;

FIG. 17 is a graph showing a relationship between a current value of anelectromagnet and a Faraday rotation angle in a third embodiment;

FIG. 18 is a graph showing a relationship between a current value of anelectromagnet and an amount of light attenuation in the thirdembodiment;

FIG. 19 is a graph showing a relationship between a current value of anelectromagnet and a Faraday rotation angle in a reference example 1;

FIG. 20 is a graph showing a relationship between a current value of anelectromagnet and an amount of light attenuation in the referenceexample 1; and

FIGS. 21A and 21B are illustrative views showing the configuration ofone example of an optical isolator.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, preferred embodiments of the present invention will bedescribed with reference to the accompanying drawings.

As a magnetooptic crystal used for a Faraday element of a Faradayrotator of the present invention, there is used a crystal having acomposition of (RBi)₃(FeM)₅O₁₂ or (RBi)₃Fe₅O₁₂ (R is one or more kindsof elements selected from a group consisting of rare earth elementsincluding yttrium; and M is one or more kinds of elements substitutablewith iron) which is manufactured by, for example, the liquid phaseepitaxial method. Typically, a crystal having a composition ofTb_(1.00)Y_(0.65)Bi_(1.35)FE_(4.05)Ga_(0.95)O₁₂ is used, and further agarnet single crystal having a composition of Y₃Fe₅O₁₂ may be used.

In a Faraday rotator of the present invention, an external magneticfield is applied to a Faraday element in such a manner as to tilt themagnetization direction of the Faraday element with respect to a lightray direction. For example, a pair of permanent magnets or anelectromagnet are arranged obliquely with respect to a light raydirection. Alternatively, there is known a configuration in whichmagnetic fields are applied to a Faraday element in two directions, onebeing parallel to, and the other being perpendicular to a light raydirection, for example, by a permanent magnet and an electromagnet,respectively.

The above-described Faraday rotator is usable for various opticaldevices such as an optical isolator, optical attenuator, optical switch,optical circulator, optical filter, and optical equalizer.

Assuming that as shown in FIG. 1A, when a light ray passes through aFaraday element 20, the magnetization direction of the Faraday element20 is tilted by an angle α with respect to the light ray direction, aFaraday rotation angle θ_(F) of the Faraday element 20 is, as isapparent from FIG. 1B, expressed by the following equation (1):

θ_(F)=θ_(Fmax)×cos α  (1)

In the above equation (1), θ_(Fmax) is the maximum value of the Faradayrotation angle, which value is obtained when the magnetization directioncorresponds to the light ray direction. The term “cos α” means that thepolarization plane of light rays is rotated only depending on acomponent of the magnetization in the light ray direction. Here, it isimportant that the magnetization direction of the Faraday element isaffected not only by the external magnetic field but also by themagnetocrystalline anisotropy of the magnetooptic crystal forming theFaraday element 20. That is to say, not only the maximum Faradayrotation angle θ_(Fmax) but also the angle α is a function of atemperature T. Accordingly, the above equation (1) can be expressed bythe following equation (2):

θ_(F)(T)=θ_(Fmax)(T)×cos α(T)  (2)

From the equation (2), the temperature coefficient of the Faradayrotation angle is given by $\begin{matrix}{\frac{\theta_{F}}{T} = {{\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} + {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} ) \times \frac{\alpha}{T}}}} & (3)\end{matrix}$

In the equation (3), assuming that the constant terms are taken asC1=cos αand C₂=θ_(Fmax)×(−sin α), the above equation (3) can beexpressed by the following equation (4): $\begin{matrix}{\frac{\theta_{F}}{T} = {{{C1} \times \frac{\quad \theta_{F\quad \max}}{T}} + {{C2} \times \frac{\alpha}{T}}}} & (4)\end{matrix}$

In the equation (4), the first term on the right side is the temperaturecoefficient of the Faraday rotation angle due to the temperaturedependence on the Faraday effect in the Faraday element, and the secondterm on the right side is the change ratio of the Faraday rotation angledue to the temperature dependence on the angle α between themagnetization direction of the Faraday element and the light raydirection. The change in the angle α is originated from the temperaturedependence on the magnetocrystalline anisotropy of the magnetoopticcrystal forming the Faraday element 20. In the case of a prior artFaraday rotator used for an optical isolator, since a sufficiently largeexternal magnetic field is applied to a Faraday element in a light raydirection, that is, the magnetization direction of the Faraday elementusually corresponds to the light ray direction, the second term on theright side of the equation (4) is usually zero, and therefore, only thetemperature coefficient of the material forming the Faraday element maybe examined.

As described above, the first term on the right side of the equation (4)is determined by the physical properties of the material forming theFaraday element and thereby the numerical value thereof cannot be variedby changing the design; however, since the second term includes theangle α, the numerical value thereof can be made large or small and alsothe sign of the numerical value can be made positive or negative bychanging the crystal orientation. To be more specific, by setting themagnetization direction to correspond to a specific orientation of theFaraday element, the sign (plus or minus) of the second term on theright side can be reversed to the sign of the first term on the rightside, to nearly cancel the amount of the change in Faraday rotationangle, thereby making small the temperature dependence on the Faradayrotation angle.

A measurement system shown in FIG. 3 was prepared, and the Faradayrotation angle of the Faraday element was measured using the measurementsystem in accordance with a polarization modulation method. In thismeasurement, the direction of the external magnetic field applied to theFaraday element, the drive current value of an electromagnet, and anenvironmental temperature were arbitrarily changed. The structure of themeasurement system is basically the same as that of an opticalattenuator. Light rays having gone out of an optical fiber 30 areconverted into parallel light rays through a lens 31, passing through apolarizer 32, a Faraday element 33, and an analyzer 34, and are focussedat an incident end of an optical fiber 36 through a lens 35. In thefigure, reference numeral 38 designates a Faraday rotator. One exampleof the Faraday rotator is shown in FIG. 4. A Faraday element 33 isapplied with a magnetic field in the direction parallel to the opticalaxis by a pair of permanent magnets 40 and 41 to be turned into amagnetic saturation state, and is applied with a magnetic field in thedirection perpendicular to the optical axis by an electromagnet 42. Thesynthetic magnetic field of the magnetic fields applied by the permanentmagnets 40 and 41 and the electromagnet 42 is varied by changing a coilcurrent flowing in the electromagnet 42. A garnet single crystal wasused for the Faraday element.

The garnet single crystal used for the Faraday element was prepared inthe following procedure. A Bi substitution rare earth iron garnet singlecrystal (LPE film, composition:Tb_(1.00)Y_(0.65)Bi_(1.35)Fe_(4.05)Ga_(0.95)O₁₂, film thickness: 450 μm)was grown onto the (111) oriented substrate( lattice constant: 12.496 Å,composition: (CaGd)₃(MgZrGa)₅O₁₂) having a diameter of 3 inches and athickness of 1170 μm using a flux of PbO—B₂O₃—Bi₂O₃ by the liquid phaseepitaxial method (LPE method). As shown in FIGS. 5A to 5D, the substrate50 is previously formed with two large and small flat planes(orientation flats). The large flat plane is the (110) plane, and thesmall flat plane is the (112) plane. In the figure, reference numeral 52designates the LPE film. The LPE film grown on the substrate 50 thusobtained was then cut into a size of 7.6 mm×5.0 mm, being polished toremove the substrate 50 therefrom, and the LPE film was annealed inatmospheric air at 1100° C. for 8 hr. The annealing is performed forreducing the growth-induced uniaxial magnetocrystalline anisotropyconstant. The LPE film was then polished again to be thusmirror-finished into a shape of 7.6 mm×5.0 mm×0.33 mm. Antireflectioncoatings were deposited on both the front and rear (111) planes of theLPE film. The LPE film was cut into a size of 1.0 mm×1.2 mm×0.33 mm.Finally, an intersection among the (111) plane, ({overscore (1)}10)plane and ({overscore (11)}2) plane was slightly cut off to form anorientation mark. The shape and faces of the final garnet single crystalare shown in FIG. 5D. A magnetic field required for realizing themagnetic saturation state of the garnet single crystal was measured bythe VSM (Vibrating Sample Magnetometer). As a result, the requiredmagnetic field was 120 Oe. On the basis of the measured result, a fixedmagnetic field of 150 Oe was applied to the garnet single crystal by apermanent magnet, to thus realize the magnetic saturation state of thegarnet single crystal. The Faraday rotation angle of the garnet singlecrystal was measured in a condition that light rays were made incidenton the garnet single crystal in the direction perpendicular to theplane, on which the antireflection coating was deposited, that is, (111)plane of the garnet single crystal. The Faraday rotation angle of thegarnet single crystal in the case where the magnetization of the garnetsingle crystal was rendered parallel to the light rays was 32°. (In thenotation for expressing the planes and orientations of a crystal, anegative index should be expressed by placing a crossbar on thenumerical value of the index; however, in this specification, thenumerical value of the index is added with a minus sign forconvenience).

FIG. 6 is a stereographic projection chart centered at the (111) planeof a garnet single crystal. In the chart, adjacent two concentriccircles indicates planes 10° offset from each other, and adjacent tworadial lines indicate planes 10° offset from each other. Any plane ofthe garnet single crystal can be indicated as a point in thestereographic projection chart.

The Faraday rotation angle of the garnet single crystal was measured byapplying a magnetic field of 150 Oe to the garnet single crystal by apermanent magnet in the vertical direction from rear to front of thepaper plane of the drawing, to thereby realize the magnetic saturationstate of the garnet single crystal; and further applying a magneticfield to the garnet single crystal by an electromagnet in a directionalong each of an “a” orientation ({overscore (11)}2) orientation), a “b”orientation (24° offset from ({overscore (11)}2 ) orientation to({overscore (1)}01) orientation), a “c” orientation ({overscore (1)}01)orientation), and a “d” orientation ({overscore (2)}11) orientation).The measurement was performed at a measurement temperature of each of10° C., 25° C. and 65° C.

The results of measuring the Faraday rotation angle are shown in FIGS. 7to 10. From the comparison between the measured results shown in FIGS. 7to 10, it is apparent that the spectrum of the Faraday rotation anglelargely varies depending on the direction of the applied magnetic field.The reason for this is due to the fact that the measured Faradayrotation angle is not only dependent on the Faraday effect but alsodependent on the magnetocrystalline anisotropy. The garnet singlecrystal has such a magnetocrystalline anisotropy that the (111)orientation and its symmetric equivalent orientation are easy axes whilethe <100> orientation and its symmetrically equivalent orientation arehard axes. The magnetocrystalline anisotropy constant becomes largerwith decreasing temperature (see P. Hansen and others: Thin Solid Films,114 (1984) 69-107).

FIG. 7 is a graph showing the result obtained in the condition that themagnetic field is applied by the electromagnet in the direction alongthe ({overscore (11)}2) orientation. In other words, the vector path ofa synthetic magnetic field of the magnetic fields applied by theelectromagnet and permanent magnet becomes the path “a” shown in FIG. 6.In the path “a”, the (001) plane is present near the center of the path,specifically, at a position 55° offset from the (111) plane. Thecross-section of the path “a” is shown in FIG. 11. Referring to FIG. 11,the magnetization of a garnet single crystal 60 is easy to be directedto the (111) orientation and the ({overscore (11)}1) orientation as theeasy axes, and is hard to be directed to the (001) orientation as thehard axis. The degree thereof becomes larger with decreasingtemperature, and accordingly, as the temperature becomes lower, themagnetization more rapidly passes through the (001) orientation andcomes closer to the ({overscore (11)}1) orientation, so that thespectrum of the Faraday rotation angle comes into that shown in FIG. 7.Referring again to FIG. 7, when the magnetic field applied by theelectromagnet becomes larger, the plus sign of the Faraday rotationangle is changed into the minus sign at a measurement temperature ofeach of 10° C. and 25° C. This is because the component of themagnetization in the light ray direction is changed from reversely toforwardly with respect to the traveling direction of the light rays. InFIG. 7, the temperature dependencies on the Faraday rotation anglemeasured at three current values of 15 mA, 20 mA and 25 mA are largelydifferent from each other. The temperature coefficient of the Faradayrotation angle is negative at the point of 15 mA; nearly zero at thepoint of 20 mA; and positive at the point of 25 mA.

Such a phenomenon will be described below. As described above, thetemperature coefficient of the Faraday rotation angle is determined onthe basis of the equation (4). As the temperature becomes higher, theFaraday effect becomes smaller and thereby the Faraday rotation anglebecomes smaller. That is to say, the temperature coefficient of theFaraday rotation angle due to the temperature dependence on the Faradayeffect, expressed by the first term on the right side of the equation(4), becomes negative. On the contrary, the temperature coefficient ofthe Faraday rotation angle due to the temperature dependence on themagnetocrystalline anisotropy, expressed by the second term on the rightside of the equation (4), differs at each current point. This isbecause, as the current value differs, the vector direction of thesynthetic magnetic field of the magnetic fields applied by theelectromagnet and permanent magnet differs (that is, the direction ofthe magnetic field applied to the Faraday element varies). At the pointof 15 mA, as the temperature becomes lower, the rotation angle α ofmagnetization becomes smaller because the magnetization of the crystalcannot approach the <001> orientation. In other words, at the point of15 mA, the rotation angle α becomes larger as the temperature becomeshigher, and therefore, the temperature coefficient expressed by thesecond term becomes negative. As a result, at the point of 15 mA, thetemperature coefficients expressed by the first and second terms areboth negative, so that the measured temperature coefficient$\frac{\theta_{F}}{T}$

of the Faraday rotation angle is also negative. At the point of 25 mA,the magnetization of the crystal cannot approach the <001> orientationas the temperature becomes lower; however, since the magnetization ofthe crystal has already passed through the <001> orientation, therotation angle α of magnetization becomes larger. In other words, at thepoint of 25 mA, the rotation angle α becomes smaller as the temperaturebecomes higher. As a result, at the point of 25 mA, the temperaturecoefficient expressed by the second terms becomes positive and furtherthe absolute value thereof is larger than that of the temperaturecoefficient expressed by the first term, so that the measuredtemperature coefficient $\frac{\theta_{F}}{T}$

of the Faraday rotation angle becomes positive. On the other hand, atthe point of 20 mA, the temperature coefficient expressed by the secondterm is positive and further the absolute value thereof is nearly equalto that of the temperature coefficient expressed by the first term, sothat both the temperature coefficients expressed by the first and secondterms can be canceled each other into approximately zero.

FIG. 8 is a graph showing the result obtained in the condition that themagnetic field is applied to the Faraday element by the electromagnet inthe direction along an orientation 24° offset from the ({overscore(1)}12) orientation to the ({overscore (1)}01) orientation. That is tosay, the vector path of a synthetic magnetic field of the magneticfields applied by the electromagnet and permanent magnet becomes thepath “b” shown in FIG. 6. Any easy axis and hard axis are not present onthe path “b” but the (001) orientation is present near the path “b”. Bythe effect of the presence of the (001) orientation near the path “b”,the first and second terms on the right side of the equation (4) arecanceled each other, and consequently the Faraday rotation anglesmeasured at 10° C., 25° C. and 65° C. are nearly equal to each other.

FIG. 9 is a graph showing the result obtained in the condition that themagnetic field is applied to the Faraday element by the electromagnet inthe direction along the ({overscore (1)}01) orientation. That is to say,the vector path of a synthetic magnetic field of the magnetic fieldsapplied by the electromagnet and permanent magnet becomes the path “c”shown in FIG. 6. The path “c” is most remote from the easy axes and hardaxes, and further, the nearest easy axes or hard axes are symmetricallypositioned with respect to the path “c”. For example, the nearest easyaxes ({overscore (11)}1) and ({overscore (1)}11) or the hard axes (001)and ({overscore (1)}00) are symmetrically positioned with respect to thepath “c”. As a result, the magnetization direction of the crystal islittle affected by the magnetocrystalline anisotropy, and therefore, itfollows a synthetic vector of vectors of the magnetic fields applied bythe electromagnet and permanent magnet. The temperature coefficient ofthe Faraday rotation angle is little dependent on the second term but onthe first term, and therefore, it becomes negative.

FIG. 10 is a graph showing the result obtained in the condition that themagnetic field by the electromagnet is applied to the Faraday element inthe direction along the ({overscore (2)}11) orientation. That is to say,the vector path of a synthetic magnetic field of the magnetic fieldsapplied by the electromagnet and permanent magnet becomes the path “d”shown in FIG. 6. In the path “d”, the ({overscore (1)}11) plane ispresent at a position 70° offset from the center, that is, the (111)plane. The magnetization of the crystal is easy to be directed to the(111) orientation and the ({overscore (1)}11) orientation as thetemperature becomes lower. When the magnetization of the crystal isdirected to the ({overscore (1)}11) orientation, the Faraday rotationangle becomes 11° on the basis of the following calculation:

θ_(Fmax)×cos 70==° ×cos 70=11

where θ_(Fmax) is the maximum Faraday rotation angle when themagnetization is directed to the light ray direction.

In the spectrum of the Faraday rotation angle shown in FIG. 10, theFaraday rotation angle is larger than that in the spectrum shown in FIG.9 on the higher current side. This is due to the fact that themagnetization of the crystal is directed to the vicinity of the({overscore (1)}11) orientation.

In this way, by applying a magnetic field to the garnet single crystalin a specific direction thereof, the sign (plus or minus) of the secondterm can be reversed to that of the first term. This makes it possibleto cancel the amounts of the changes in the Faraday rotation angle dueto the first and second terms each other and hence to make smaller thetemperature dependence on the Faraday rotation angle. The magnetic fieldmay be applied in a single specific direction as shown in FIGS. 7 and 8.Alternatively, in consideration of the fact that the spectra of theFaraday rotation angles shown in FIGS. 7 to 10 are largely differentfrom each other, a plurality of garnet single crystals may be used forthe Faraday element, and the magnetic field may be applied to eachcrystal in an arbitrary direction in such a manner that the totaltemperature dependencies on the Faraday rotation angle are made smaller.

Based on the symmetry of the crystal, as shown in FIG. 6, the change inFaraday rotation angle due to the applied magnetic field by theelectromagnet in the direction along the ({overscore (11)}2) that is,the path “a” is the same as that due to the applied magnetic field bythe electromagnet in the direction along the orientation symmetricallyequivalent to the ({overscore (11)}2) that is, the ({overscore (1)}21)orientation or the ({overscore (2)}11) orientation 120° offset from the({overscore (11)}2) orientation. The same is true for each of the paths“b” to “d”.

The present invention will be more fully described by example of thefollowing embodiments:

First Embodiment

A measurement system as shown in FIG. 3 was manufactured. Using themeasurement system, the temperature dependence on the Faraday rotationangle of a Faraday element was measured by a polarization modulationmethod, and then the temperature dependence on the amount of lightattenuation was measured in a condition that the polarizer and theanalyzer were fixed with an angle between polarization planes of lightrays passing therethrough set at 135° . The magnetic field applied by apermanent magnet was set at 150 Oe, and the drive current of anelectromagnet was fixed at 20 mA. The structure of the measurementsystem is basically the same as that of an optical isolator, andtherefore, the amount of light attenuation is equivalent to thebackward-loss.

A garnet single crystal used for the Faraday element was manufactured inthe procedure shown in FIGS. 5A to 5D. A Bi substitution rare earthelement-iron garnet single crystal (LPE film, composition:Tb_(1.00)Y_(0.65)Bi_(1.35)Fe_(4.05)Ga_(0.95)O₁₂, film thickness: 450 μm)was grown onto the (111) oriented substrate having a diameter of 3inches and a thickness of 1170 μm using a flux of PbO—B₂O₃—Bi₂O₃ by theLPE method. In addition, the above substrate has a lattice constant of12.496 Å and a composition of (CaGd)₃(MgZrGa)₅O₁₂. As shown in FIGS. 5Ato 5D, the substrate is previously formed with two large and small flatplanes. The large flat plane is the ({overscore (1)}10) plane, and thesmall flat plane is the (11{overscore (2)}) plane. The LPE film grown onthe substrate thus obtained was then cut into a size of 7.6 mm×5.0 mm,being polished to remove the substrate therefrom, and the LPE film wasannealed in atmospheric air at 1100° C. for 8 hr. The annealing isperformed for reducing the uniaxial magnetocrystalline anisotropyconstant due to growth induction. The LPE film was then polished againto be thus mirror-finished into a shape of 7.6 mm×5.0 mm×0.35 mm.Antireflection coatings were deposited on both the front and rear (111)planes of the LPE film. The LPE film was cut into a size of 1.0 mm×1.2mm×0.35 mm. Finally, an intersection among the (111) plane, ({overscore(1)}10) plane and ({overscore (11)}2) plane was slightly cut off to forman orientation mark. A magnetic field required for realizing themagnetic saturation state of the garnet single crystal was measured bythe VSM (Vibrating Sample Magnetometer). As a result, the requiredmagnetic field was 120 Oe. On the basis of the measured result, a fixedmagnetic field of 150 Oe was applied to the garnet single crystal by apermanent magnet, to thus realize the magnetic saturation state of thegarnet single crystal. The Faraday rotation angle of the garnet singlecrystal was measured in a condition that light rays were made incidenton the garnet single crystal in the direction perpendicular to theplane, on which the antireflection coating was deposited, that is, (111)plane of the garnet single crystal.

As shown in FIG. 12A, a Faraday element 70 was prepared by arrangingthree pieces of magnetic garnet single crystals 72 manufactured asdescribed above with the orientations aligned with each other such thatthe ({overscore (11)}2) planes on the chamfered sides are arranged onthe S-pole side of the electromagnet. That is to say, the magnetic fieldis applied in the ({overscore (11)}2) orientation by the electromagnet.This is equivalent to the case where the current of the electromagnet isset at 20 mA in the path “a” shown in FIG. 7. The garnet single crystalhas a Faraday rotation angle of about 34° when the magnetization isdirected to the direction parallel to light rays, and accordingly, theFaraday element has a Faraday rotation angle of 34°×3=102°. The reasonwhy three pieces of the garnet single crystals are used in thisembodiment is that since the thickness of the garnet single crystal cutfrom the grown crystal having a film thickness of 450 μm becomes thin,the Faraday rotation angle per one garnet single crystal becomes small.At the present day, it is difficult to grow a garnet single crystal upto a thickness more than 500 μm without occurrence of defects and cracksby the LPE method. However, if the crystal growth technique will advanceto grow a garnet single crystal up to a thickness more than 500 μmwithout occurrence of defects and cracks, and hence to make large theFaraday rotation angle of one crystal by increasing the thickness of onegarnet single crystal after being cut from the grown crystal, the numberof the garnet single crystals used may be two pieces or one piece.

The garnet single crystal was applied with a magnetic field by anelectromagnet in the direction perpendicular to a light ray direction,and was applied with a magnetic field by a permanent magnet in thedirection parallel to the light ray direction. The result of measuringthe Faraday rotation angle is shown in FIG. 13, and the result ofmeasuring the amount of light attenuation is shown in FIG. 14. From theresults shown in FIGS. 13 and 14, it is apparent that both the Faradayrotation angle and the amount of light attenuation in the firstembodiment have small temperature dependence, and therefore, the Faradayrotator is advantageous when used for an optical isolator. In the caseof actually manufacturing the optical isolator, the magnetization of themagnetic garnet single crystals may be tiled with respect to the opticalaxis using the permanent magnet and electromagnet as in this embodiment;the magnetization of the magnetic garnet single crystals may be tiledwith respect to the optical axis by arranging a pair of permanentmagnets obliquely with respect to the optical axis; or the magnetizationof the magnetic garnet single crystals may be tilted with respect to theoptical axis by arranging one cylindrical permanent magnet obliquelywith respect to the optical axis and placing the magnetic garnet singlecrystals in the permanent magnet with the deposited plane, that is,(111) plane of each of the single crystals directed perpendicularly tothe optical axis. In each case, the same effect can be obtained, thatis, the temperature dependence on the Faraday rotation angle can be madesmaller.

A comparative example A shown in FIGS. 13 and 14 was manufactured in thefollowing procedure, and then measured. A Faraday element was preparedby using two pieces of magnetic garnet single crystals, each having athickness of 0.233 mm, which were manufactured in the same manner asthat in the first embodiment. The Faraday element has a Faraday rotationangle of about 45° when the magnetization direction was renderedparallel to a light rays direction. The Faraday rotation angle and theamount of light attenuation were measured in a condition that theelectromagnet was removed from the measurement system shown in FIG. 3and only a magnetic field was applied to the crystal by the permanentmagnet. Each of the two magnetic garnet single crystals was arrangedsuch that light rays were made incident on the crystal in the directionperpendicular to a plane on which an antirefraction coating wasdeposited, that is, (111) plane of the garnet single crystal. Themagnetization of each magnetic garnet single crystal was saturated bythe permanent magnet, and was directed to the direction parallel to theoptical axis. First, the temperature dependence on the Faraday rotationangle was measured by the polarization modulation method, and then thetemperature dependence on the amount of light attenuation was measuredin a condition that the polarizer and analyzer were fixed with an anglebetween the polarization planes of light rays passing therethrough setat 135°. The structure of the measurement system is basically the sameas that of the prior art optical isolator, and therefore, the amount oflight attenuation is equivalent to the backward loss.

Second Embodiment

A garnet single crystal having a size of 1.0 mm×1.2 mm×0.33 mm wasmanufactured in the same procedure as that in the first embodiment. Thegarnet single crystal has a Faraday rotation angle of about 32° when themagnetization is directed to the direction parallel to a light raydirection. Using the measurement shown in FIG. 3, the temperaturedependence on the Faraday rotation angle was measured by thepolarization modulation method, and then the temperature dependence onthe amount of light attenuation was measured in a condition that thepolarizer and the analyzer were arranged with an angle between thepolarization planes of light rays passing therethrough set at 105°. Themagnetic field of a permanent magnet was set at 150 Oe, and the drivecurrent of an electromagnet was variable in a range of 0 to 80 mA. Thestructure of the measurement system is basically the same as that of anoptical attenuator. As shown in FIG. 12B, a Faraday element 74 wasprepared by arranging three pieces of magnetic garnet single crystals 72manufactured as described above with the orientations changed such thatthe ({overscore (11)}2) plane, on the chamfered side, of the frontgarnet single crystal was located on the S-pole side of theelectromagnet and the ({overscore (11)}2) planes, on the chamfered side,of the rear two garnet single crystals were located on the N-pole sideof the electromagnet. The garnet single crystal was applied with amagnetic field by the electromagnet in the direction perpendicular tothe light ray direction and was applied with a magnetic field by thepermanent magnet in the direction parallel to the light rays direction.This means that each of the rear two garnet single crystals is appliedwith the magnetic field in the direction along a line, in astereographic projection chart, which connects the center expressing the(111) plane to a position expressing the (11{overscore (2)}) plane onthe outermost peripheral circle, and the front magnetooptical crystal isapplied with the magnetic field in the direction along a line, in thestereographic projection chart, which connects the center expressing the(111) plane to a position expressing the ({overscore (11)}2) plane onthe outermost peripheral circle.

The result of measuring the Faraday rotation angle is shown in FIG. 15and the result of measuring the amount of light attenuation is shown inFIG. 16. From the result shown in FIG. 15, it is apparent that thetemperature dependence on the Faraday rotation angle is small when alarge current is applied to the electromagnet. From the result shown inFIG. 16, it is apparent that the temperature dependence on the amount oflight attenuation is small. As a result, the above configuration in thisembodiment is effective for a magnetooptic type variable opticalattenuator.

Third Embodiment

A garnet single crystal having a size of 1.0 mm×1.2 mm×0.33 mm wasmanufactured in the same procedure as that in the first embodiment. Thegarnet single crystal has a Faraday rotation angle of about 32° when themagnetization is directed to the direction parallel to a light raydirection. Using the measurement system shown in FIG. 3, the temperaturedependence on the Faraday rotation angle was measured by thepolarization modulation method, and then the temperature dependence onthe amount of light attenuation was measured in a condition that thepolarizer and the analyzer were arranged with an angle between thepolarization planes of light rays passing therethrough set at 105°. Themagnetic field of a permanent magnet was set at 150 Oe, and the drivecurrent of an electromagnet was variable in a range of 0 to 80 mA. Thestructure of the measurement system is basically the same as that of anoptical attenuator. As shown in FIG. 12A, a Faraday element 70 wasprepared by arranging three pieces of magnetic garnet single crystals 72manufactured as described above with the orientations aligned with eachother, and was applied with a magnetic field by the electromagnet in thedirection along an orientation 24° offset from the ({overscore (11)}2)orientation to the ({overscore (1)}01) orientation. The garnet singlecrystal was applied by the electromagnet in the direction perpendicularto the light ray direction, and was applied with a magnetic field by thepermanent magnet in the direction parallel to the light ray direction.This means that the magnetooptic crystal is applied with the magneticfield in the direction along a line, in a stereographic projectionchart, which connects the center expressing the (111) plane to aposition, on the outermost peripheral circle, 24° offset from the({overscore (11)}2) orientation to the ({overscore (1)}01) orientation.

The result of measuring the Faraday rotation angle is shown in FIG. 17and the result of measuring the amount of light attenuation is shown inFIG. 18. From the result shown in FIG. 17, it is apparent that thetemperature dependence on the Faraday rotation angle is small. From theresult shown in FIG. 18, it is apparent that the temperature dependenceon the amount of light attenuation is small. As a result, the aboveconfiguration in this embodiment is effective for a magnetooptic typevariable optical attenuator.

REFERENCE EXAMPLE 1

A garnet single crystal having a size of 1.0 mm×1.2 mm×0.33 mm wasmanufactured in the same procedure as that in the first embodiment. Thegarnet single crystal has a Faraday rotation angle of about 32° when themagnetization is directed to the direction parallel to a light raydirection. Using the measurement system shown in FIG. 3, the temperaturedependence on the Faraday rotation angle was measured by thepolarization modulation method, and then the temperature dependence onthe amount of light attenuation was measured in a condition that thepolarizer and the analyzer were arranged with an angle between thepolarization planes of light rays passing therethrough set at 105°. Themagnetic field applied by a permanent magnet was set at 150 Oe, and thedrive current of an electromagnet was variable in a range of 0 to 80 mA.The structure of the measurement system is basically the same as that ofan optical attenuator. As shown in FIG. 12A, a Faraday element wasprepared by arranging three pieces of single crystals manufactured asdescribed above with the orientations thereof aligned with each othersuch that the ({overscore (1)}10) planes thereof were located on theS-pole side of the electromagnet. That is to say, the magnetic field isapplied by the electromagnet in the direction along the ({overscore(1)}10) orientation. The garnet single crystal was applied with themagnetic field by the electromagnet in the direction perpendicular tothe light ray direction, and was applied with the magnetic field by thepermanent magnet in the direction parallel to the light ray direction.

The result of measuring the Faraday rotation angle is shown in FIG. 19and the result of measuring the amount of light attenuation is shown inFIG. 20. From the results shown in FIGS. 19 and 20, it is apparent thatthe temperature dependence on each of the Faraday rotation angle and theamount of light attenuation is large. As seen from this result, theabove configuration in this reference example 1 is unsuitable for amagnetooptic type variable optical attenuator.

While the preferred embodiments of the present invention have beendescribed using the specific terms, such description is for illustrativepurposes only, and it is to be understood that changes and variationsmay be made without departing from the spirit or scope of the followingclaims.

What is claimed is:
 1. A Faraday rotator comprising: a Faraday elementwhich rotates the polarization plane of polarized light rays passingthrough said Faraday element when an external magnetic field is appliedto said Faraday element, characterized in that the direction of saidexternal magnetic field has been adjusted to satisfy the followingconditions “A” and “B” regarding$\frac{\theta_{F}}{T} = {\lbrack {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} )\frac{\alpha}{T}} \rbrack + \lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack}$

that is the change of Faraday rotation angle per change of temperature,when the angle between the resultant magnetization direction of saidFaraday element and the direction of the polarized light rays isrepresented by α, the resultant Faraday rotation angle is expressed asθ_(F)=θ_(Fmax)×cosα, wherein θ_(Fmax) is the maximum value of theFaraday rotation angle, which value is obtained when the magnetizationdirection is equal to the light ray direction, and wherein saidresultant magnetization is due to said external magnetic field and saidFaraday element wherein, condition A is:${{\lbrack {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} )\frac{\alpha}{T}} \rbrack + \lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack} < 0},$

where “T” represents the temperature; and, condition B is: the absolutevalue of one of the first amount$\lbrack {{\overset{.}{\theta}}_{F\quad \max} \times ( {{- \sin}\quad \alpha} ) \times \frac{\alpha}{t}} \rbrack$

and second amount$\lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack$

is less than twice the absolute value of the other amount.
 2. A Faradayrotator comprising: a Faraday element composed of a single or aplurality of magnetooptic crystals, which rotates the polarization planeof polarized light rays passing through said Faraday element when aneternal magnetic field is applied to said Faraday element, characterizedin that the direction of said external magnetic field has been adjustedso as to satisfy the following conditions “C” and “D” regarding${\frac{\theta_{F}}{T} = {\lbrack {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} ) \times \frac{\alpha}{T}} \rbrack + \lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack}},$

that is the change of Faraday rotation angle per change of temperature,when the angle between the resultant magnetization direction of saidsingle or plurality of magnetooptic crystals and the direction of thepolarized light rays is represented by α, the resultant Faraday rotationangle is expressed as θ_(F)=θ_(Fmax)×cosα, wherein θ_(Fmax) is themazimum value of the Faraday rotation angle, which value is obtainedwhen the magnetization direction is equal to the light ray direction,and wherein said external magnetic field is applied in a singledirection, wherein condition is:${{\lbrack {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} ) \times \frac{\alpha}{T}} \rbrack \times \lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack} < 0},$

wherein “T” represents the temperature; and, condition D is the absolutevalue of one of the first amount$\lbrack {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} ) \times \frac{\alpha}{T}} \rbrack$

and second amount$\lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack$

is less than twice the absolute value of the other amount.
 3. A Faradayrotator according to claim 1 or 2, characterized in that the directionof said external magnetic field is such that said first amount$\lbrack {\theta_{F\quad \max} \times ( {{- \sin}\quad \alpha} ) \times \frac{\alpha}{T}} \rbrack$

and said second amount$\lbrack {\cos \quad \alpha \times \frac{\theta_{F\quad \max}}{T}} \rbrack$

have substantially equal absolute values.
 4. A Faraday rotatorcomprising: a Faraday element which rotates the polarization plane ofpolarized light rays passing through said Faraday element when anexternal magnetic field is applied to said Faraday element, wherein amagnetooptic crystal constituting said Faraday element has a compositionof Tb_(1.00)Y_(0.65)Bi_(1.35)Fe_(4.05)Ga_(0.95)O₁₂; and the amount ofthe temperature-dependent change in Faraday rotation angle is reduced byapplying magnetic field to said magnetooptic crystal in a directionalong a line, in a stereographic projection chart of said magnetoopticcrystal, which connects the center expressing the (111) plane to aposition 24° offset from the ({overscore (11)}2) plane to the({overscore (1)}01) plane on the outermost peripheral circle of thestereographic projection chart.
 5. A Faraday rotator comprising: aFaraday element which rotates the polarization plane of polarized lightrays passing through said Faraday element when an external magneticfield is applied to said Faraday element, wherein said Faraday elementis composed of three pieces of magnetooptic crystals each of which has acomposition of Tb_(1.00)Y_(0.65)Bi_(1.35)Fe_(4.05)Ga_(0.95)O₁₂ and has asubstantially equal thickness; and the amount of thetemperature-dependent change in Faraday rotation angle is reduced byapplying magnetic field to to pieces of said magnetooptic crystals in adirection along a line, in a stereographic projection chart of saidmagnetooptic crystal, which connects the center expressing the (111)plane to the (11{overscore (2)}) plane on the outermost peripheralcircle, and applying magnetic field to the remaining magnetoopticcrystal in a direction along a line, in stereographic projection chart,which connects the center expressing the (111) plane to the(11{overscore (2)}) plane on the outermost peripheral circle.
 6. AFaraday rotator comprising: a Faraday element composed of a plurality ofmagnetooptic crystals arranged with their crystal orientations madedifferent from each other, which rotates the polarization plane ofpolarized light rays passing through said Faraday element when anexternal magnetic field is applied to said Faraday element, wherein thetotal number of said plurality of magnetooptic crystals are representedby “k”, characterized in that the direction of said external magneticfield has been adjusted so as to satisfy the following condition “E”regarding${\frac{\theta_{F}}{T} = {{\sum\limits_{i = 1}^{k}\lbrack {\theta_{f\quad i\quad \max} \times ( {{- \sin}\quad \alpha_{i}} ) \times \frac{\alpha_{i}}{T}} \rbrack} + {\sum\limits_{i = 1}^{k}\lbrack {\cos \quad \alpha_{i} \times \frac{\theta_{{Fi}\quad \max}}{T}} \rbrack}}},$

that is the change of Faraday rotation angle per change of temperature,when the angles between magnetization directions M_(i) of saidmagnetooptical crystals C_(i) and a light ray transmission direction arerepresented by α_(i), wherein “i” represents all of the natural numbersfrom 1 through k, the resultant Faraday rotation angle is expressed as${\theta_{F} = {{\sum\limits_{i = 1}^{k}\theta_{Fi}} = {\sum\limits_{i = 1}^{k}( {\theta_{{Fi}\quad \max} \times \cos \quad \alpha_{i}} )}}},$

wherein θ_(Fimax) is the maximum value of the Faraday rotation angle ofsaid crystal C_(i), which value is obtained when the magnetizationdirection M_(i) of said crystal C_(i) is equal to the light raydirection, wherein condition E is:${{\sum\limits_{i = 1}^{k}\lbrack {{\theta_{{Fi}\quad \max} \times ( {{- \sin}\quad \alpha_{i}} )\frac{\alpha_{i}}{T}} + {\cos \quad \alpha_{i} \times \frac{\theta_{{Fi}\quad \max}}{T}}} \rbrack}} \leq {{{\sum\limits_{i = 1}^{k}\lbrack {\cos \quad \alpha_{i} \times \frac{\theta_{{Fi}\quad \max}}{T}} \rbrack}}.}$


7. A Faraday rotator according to any one of claims 1 or 2, and 6,wherein said magnetooptic crystal is grown by liquid phase epitaxialmethod and has a composition of (RBi)₃(FeM)₅O₁₂ or (RBi)₃Fe₅O₁₂ where Ris one or more kinds of elements selected from the group consisting ofrare earth elements and M is one or more kinds of elements substitutablewith iron.
 8. A Faraday rotator according to any one of claims 1, 2, and6, wherein said magnetooptic crystal has a composition of Y₃Fe₅O₁₂. 9.An optical isolator comprising: a Faraday rotator which is the same assaid Faraday rotator described in any one of claims 1, 2, 6, 4, and 5.10. An optical attenuator comprising: a Faraday rotator which is thesame as said Faraday rotator described in any one of claims 1, 2, 6, 4,and
 5. 11. A Faraday rotator according to any one of claims 1, 2, 6, 4,and 5, wherein external magnetic fields are applied in directionsparallel to and perpendicular to a light ray direction by a permanentmagnet and an electromagnet, and a magnetization direction of saidFaraday element is tilted with respect to the light ray direction by asynthetic magnetic field of said two external magnetic fuels.
 12. Amethod of controlling the temperature dependence on a Faraday rotatorwhich is the same as said Faraday rotator described in claim 11,comprising the step of: controlling the temperature dependence on theFaraday rotation angle by changing a magnetic field applied by saidelectromagnet.
 13. An optical isolator comprising: a Faraday rotatorwhich is the same as said Faraday rotator described in claim 11, and apolarizer and an analyzer arranged on the front and rear sides of saidFaraday rotator in the light ray direction; wherein a magnetic fieldapplied by said electromagnet is set such that the temperaturedependence on the Faraday rotation angle is minimized.
 14. An opticalattenuator comprising: a Faraday rotator which is the same as saidFaraday rotator described in claim 11, and a polarizer and an analyzerarranged on the front and rear sides of said Faraday rotator in thelight ray direction; wherein an external magnetic field applied by saidelectromagnet is variable, and the quantity of light rays passingtherethrough is controlled by varying said external magnetic field.